Scatter Plots and Linear Correlation ( Read ) | Statistics | CK Foundation
Examining a scatterplot graph allows us to obtain some idea about the relationship between two variables. When the points on a scatterplot. The individual values can be read from the plot and an idea of the relationship between the variables across individuals is obtained. Even if the plot is not used . Business Statistics For Dummies. By Alan Anderson. A scatter plot (also known as a scatter diagram) shows the relationship between two quantitative.
The line of equality no change in values pre to during treatment is shown as a dashed line on the display. All points lie above the line of equality showing that values rose for each individual. Whilst the same information is given by the two displays, the scatterplot uses only one point to represent each individual compared to 2 points and a line for the line diagram.
Describing scatterplots (form, direction, strength, outliers)
The line diagram may be confusing to assess if there are changes in various directions, the scatterplot with the line of equality superimposed if necessary is easier to interpret. No information is lost, the display clearly shows the relationship between the variables and also highlights possible outliers.
- Scatter Plots
We saw an example earlier of the times it takes for a scorpion to capture its prey presented as a dot plot. Optimal sting use in the feeding behavior of the scorpion Hadrurus spadix. Dot plots can also be used to look at the differences between the distributions of groups.
In the example below, E coli specific SigA values are typically lower and also less spread out in the 'White UK' category. Dot plots can be used to look at whether values in one group are typically different from values in another group. In the example above, the plot shows it typically takes slightly longer for a scorpion to catch a prey with low activity than high activity.
Archives of Disease in Childhood,;71,F Horizontal bars denote medians for each group. The table below shows how social class varied between the two areas of the baby check scoring system. In both areas the mothers were mostly from social class III manual. This table shows how illness severity was related to baby-check score.
Describing scatterplots (form, direction, strength, outliers) (article) | Khan Academy
We can see the association of increasing severity with increasing score. The initial impression was not recorded for two babies. Neonatal morbidity and care-seeking behaviour in rural Bangladesh.
Journal of Tropical Pediatrics,47, Amongst other things, the first table below shows how medically unqualified practitioners were used most often for all recorded forms of morbidity and for more than one in three skin rashes no care was sought. In the second table we see that care from the district hospital appears to be the most expensive option, followed by private practitioners and village doctors.
Three dimensional bar-charts can be used to show the numbers in each section of the table. However, whilst these may look quite impressive, they do not generally make interpretation any simpler and may even 'lose the numbers'. Cardia et al, Outcome of craniocerebral trauma in infants and children, Childs Nerv. The information shown above gender and age group could be given in a 2x3 table two rows: The three dimensional bar-chart replaces each of the six numbers with a bar of the appropriate height; however, because of the three dimensional aspect of the display it is not possible to read off the original numbers.
The display is used to impart only 6 figures, and it has lost those!
Graphical Displays: Two Variables
It appears that for most of the years ozone was the major component of air quality standard. In sulphur dioxide was the main feature.
It is not possible to read off the actual figures. This data could have been shown as a 7x5 table. These displays may look impressive, but they are not generally an effective way of imparting the information with minimal loss of relevant information. Side-by-side or stacked bar charts may be an effective way of presenting data on two categorical variables. A perfect negative correlation is given the value of If there is absolutely no correlation present the value given is 0. The closer the number is to 1 or -1, the stronger the correlation, or the stronger the relationship between the variables.
The closer the number is to 0, the weaker the correlation. So something that seems to kind of correlate in a positive direction might have a value of 0. An example of a situation where you might find a perfect positive correlation, as we have in the graph on the left above, would be when you compare the total amount of money spent on tickets at the movie theater with the number of people who go.
This means that every time that "x" number of people go, "y" amount of money is spent on tickets without variation. An example of a situation where you might find a perfect negative correlation, as in the graph on the right above, would be if you were comparing the amount of time it takes to reach a destination with the distance of a car traveling at constant speed from that destination.
On the other hand, a situation where you might find a strong but not perfect positive correlation would be if you examined the number of hours students spent studying for an exam versus the grade received. This won't be a perfect correlation because two people could spend the same amount of time studying and get different grades. But in general the rule will hold true that as the amount of time studying increases so does the grade received.
Let's take a look at some examples.